My collaborators are using Matlab to do some simulations. Is there an open source alternative I could use on Linux to run these scripts? It would need to be fairly closely compatible with the (1) matlab language (2) the *.fig files - saved plots.

Interestingly it looks like Wolfram Alfa has an entry into the field that runs on Linux, although the license is proprietary. After that the popular ones appear to be Sage, Octave and Scilab, although you should check through the list to see if anything suits you better as there are some promising names such as FreeMat and OpenModelica (although if the projects are immature they could be disappointing.)

I have tried Octave and Scilab and 90% of the time, my code runs on MATLAB without a single modification. Sometimes, there are a few modifications necessary but they are well documented and quite easy to implement. (Like % as comments instead of // etc.)

Between Octave and SciLab, A quick google search will help you find one that suits your need. But both are brilliant IMO.